Mathematical framework for place coding in the auditory system

Abstract

A distinct feature of the auditory system is the tonotopic organization where the preferred frequency of neurons changes systematically along one axis. Tonotopy is postulated to be substrate for a place code, where sound frequency is encoded by the location of the neurons that fire during the stimulus. Though conceptually simple, the computations that allow for the representation of intensity and complex sounds is poorly understood. Here, the mathematical framework for place code is developed. The analyses suggest that the functional architecture, or topology, consists of overlapping neuron clusters whose size varies with intensity. Algebraic operations are derived to elucidate the rules for representing and assembling multi-frequency sound in networks and for modulating them with inhibition. Results obtained with network simulations are consistent with the general predictions. The analyses reveal the advantages and limitations of a place code and provide a mathematical foundation for building computational models and for interpreting experimental data.

Topological conditions for propagation of spatially-distributed neural activity

“…1a). The partitioning of neural space into units of neurons described previously [16] is extended to 2 dimensions (see Appendix). Visually, the neural space is a 'half-open' box with the bottom and left edges closed and the top and right edges open (Fig.…”

“…Biological neural networks are composed of neurons that are embedded in and separated by extracellular matrix. Because the neurons are the functional units, the neural space and associated sensory representation are essentially discretized [16]. To facilitate formal analyses, we disregard the extracellular matrix and construct the neural space with a grid-like architecture.…”

“…In this study, the size of the synaptic fields were kept constant and instead, the 'cloud' of active neurons was varied to reflect changes in e.g. the intensity of the stimulus [16]. The resultant Čech complexes changed accordingly, as did the Betti numbers.…”

“…The Betti numbers can be used to as a basis for initial categorization of spatial activity patterns. In the auditory system, for example, the location and size of the activated area may be used to encode the frequency and intensity of tones [16]. Psychophysical experiments show that the perceived frequency of a tone changes little with intensity [30].…”